German Chancellor Angela Merkel has said her country must remain "clever and cautious" in handling the coronavirus crisis, as it is "not the end phase but still just the beginning".
"We'll have to live with this virus for a long time," Ms Merkel told parliament ahead of an EU summit, via videolink.
She said Germany should be ready to "make very different, meaning much higher contributions to the EU budget".
The video summit - the EU's fourth on coronavirus - is now under way.
EU leaders are expected to sign off on a new €540bn (£470bn; $575bn) emergency fund to protect European workers, businesses and countries worst affected by the coronavirus outbreak. The details are yet to be worked out.
The €540bn would be released through EU institutions that already exist, including the European Stability Mechanism (ESM), the main bailout fund set up in response to the 2008 financial crisis.
European Council President Charles Michel told leaders they should aim to start releasing the funds by 1 June.
But a thornier issue is how much extra to commit to the EU budget to deal with this crisis, and how much the 27 member states will spend jointly. There are plans for a special recovery fund, like the post-1945 Marshall Plan.
Italy and some other states want EU help in aid grants, not loans. The scale of the crisis is such, they argue, that at least €1.5 trillion will be needed.
Mrs Merkel said extra EU budget funds should be provided "in a spirit of solidarity" and for a limited time.
Italy, at the epicentre of the pandemic in Europe, has been especially vocal in urging its EU partners to jointly guarantee debt.
But Germany, the Netherlands and Austria oppose any mutualisation of debt, in the form of so-called "coronabonds". Under current EU rules countries cannot be made liable for each other's debts.
Many Italians feel abandoned by the EU
The old rifts from the eurozone crisis of 2009 - a supposedly frugal northern Europe versus a spendthrift south - have re-emerged with this outbreak.
The view from Rome is that a shared crisis needs a shared solution. Facing fierce opposition mainly from Germany and the Netherlands, Italy may no longer be wedded to its idea of "coronabonds" - debt mutualisation - but is still pushing for a financial package that does not penalise any single economy. That, after all, is the spirit of the common market that Italy helped create.
Many Italians feel abandoned by an EU that has hoarded protective equipment and closed borders.
Polls show anti-EU feeling is at its highest ever here. The leader of the hard-right Brothers of Italy party, Giorgia Meloni, told me the EU had shown its inadequacy and distance from the solidarity its members craved, peddling the idea of Italy as a beggar, wasting its money.
"The EU exists thanks to Italy," she said. "But it's now a system that favours others." Hers is the party steadily rising in the polls.
French President Emmanuel Macron has sided with Italy and Spain in this crisis, warning that it threatens the very existence of the EU. Italy, Spain and France - in that order - have the highest European death tolls from Covid-19, each above 20,000.
On Thursday German officials said coronavirus cases nationally had risen to 148,046, and the number of deaths linked to Covid-19 had risen by 215 to 5,094.
Mrs Merkel said "it's the biggest challenge since World War Two, for the life and health of our people".
She urged "maximum discipline", to avoid stop-start lockdowns.
"We must not waste what has been achieved already," she said, praising the efficiency of Germany's healthcare system and the armed forces' role.
"The question of how we can prevent the virus from overwhelming our health system and subsequently costing the lives of countless people, this question will for a long time be the central question for politics in Germany and Europe."
The World Health Organization (WHO) says care home residents account for up to half of Covid-19 deaths in Europe, which is "a deeply concerning picture".
Mrs Merkel said Europe must strengthen its capacity to produce specialised medical kit, instead of depending on global supplies, which are now very stretched.
She also called the WHO an indispensable partner in the fight against the virus. President Donald Trump has suspended US funding of the body.
"I know how difficult the restrictions are, it's a challenge to democracy, it limits our democratic rights," she said, adding that democratic transparency, such as a free press, helped to make the situation tolerable.
"It's amazing how much understanding people have shown for each other," she said. MPs frequently applauded her.